Question

Use technology to construct the confidence intervals for the population variance

sigmaσsquared2

and the population standard deviation

sigmaσ.

Assume the sample is taken from a normally distributed population.

cequals=0.95

ssquared2equals=12.96

nequals=25

Answer 1

Solution :

Given that,

Point estimate = s² = 12.96

$\chi$²_L = $\chi$ ²_{$\alpha$/2,df} = 39.364

$\chi$²_R = $\chi$ ²_{1 - $\alpha$ /2,df} = 12.401

The 95% confidence interval for $\sigma$ ² is,

(n - 1)s² / $\chi$ ²_$\alpha$/2 < $\sigma$ ² < (n - 1)s² / $\chi$ ²_{1 - $\alpha$ /2}

24 * 12.96 / 39.364 < $\sigma$ ² < 24 * 12.96 / 12.401

7.90 < $\sigma$ ² < 25.08

(7.90 , 25.08)

The 95% confidence interval for $\sigma$ is,

2.81 < $\sigma$ < 5.01

(2.81 , 5.01)